Output from imlmat1.sas	Source 0 Graphs

NOTE: Capture of log output started.

NOTE: %INCLUDE (level 1) file n:\psy6140\examples\iml\imlmat1.sas is file
      n:\psy6140\examples\iml\imlmat1.sas.

675  +title 'IMLMAT1: Basic matrix definitions';
676  +options nodate;
677  +proc iml;

IML Ready

678  +   reset print log;
679  +
680  +   *-- Matrix: a rectanglar array of numbers;
681  +   X = {1 2 3, 4 0 6, 9 1 4, 6 2 4};

                X             4 rows      3 cols    (numeric)

                                1         2         3
                                4         0         6
                                9         1         4
                                6         2         4

682  +
683  +   print (nrow(X)) (ncol(X));

                              #TEM1001  #TEM1002
                                     4         3

684  +   rowvec = { 1 2 3};

                ROWVEC        1 row       3 cols    (numeric)

                                1         2         3

685  +   colvec = { 1, 4, 6};

                COLVEC        3 rows      1 col     (numeric)

                                          1
                                          4
                                          6

686  +   *-- transpose: interchanges rows and cols;
687  +   xt = x`;

                XT            3 rows      4 cols    (numeric)

                           1         4         9         6
                           2         0         1         2
                           3         6         4         4

688  +   xt = t(x);

                XT            3 rows      4 cols    (numeric)

                           1         4         9         6
                           2         0         1         2
                           3         6         4         4

689  +   *-- square matrix: same number of rows and cols;
690  +   A = {5 -1 3, -1 4 7, 3 3 -4};

                A             3 rows      3 cols    (numeric)

                                5        -1         3
                               -1         4         7
                                3         3        -4

691  +   *-- main diagonal: entries A[i,i];
692  +   d = vecdiag(A);

                D             3 rows      1 col     (numeric)

                                          5
                                          4
                                         -4

693  +   *-- diagnonal matrix: all zero except for main diagonal;
694  +   d = diag({1 4 9});

                D             3 rows      3 cols    (numeric)

                                1         0         0
                                0         4         0
                                0         0         9

695  +   *-- trace: for square matrix, the sum of main diagonal;
696  +   t = trace(A);

                T             1 row       1 col     (numeric)

                                          5

697  +   *-- symmetric matrix: square, and equal to its transpose
698  +       i.e., A[i,j] = A[j,i];
699  +   sym = ( A = A` );

                SYM           3 rows      3 cols    (numeric)

                                1         1         1
                                1         1         0
                                1         0         1

700  +   sym = all( A = A` );

                SYM           1 row       1 col     (numeric)

                                          0

701  +   *-- any square matrix may be made symmetric by averaging
702  +       with its transpose;
703  +   B = ( A + A` ) / 2;

                B             3 rows      3 cols    (numeric)

                                5        -1         3
                               -1         4         5
                                3         5        -4

704  +   sym = all( B = B`);

                SYM           1 row       1 col     (numeric)

                                          1

705  +   *-- upper triangular matrix: all below main diag = 0;
706  +   upper = {-5 2 7, 0 -2 4, 0 0 3};

                UPPER         3 rows      3 cols    (numeric)

                               -5         2         7
                                0        -2         4
                                0         0         3

707  +   *-- lower triangular matrix: all below main diag = 0;
708  +   lower = upper`;

                LOWER         3 rows      3 cols    (numeric)

                               -5         0         0
                                2        -2         0
                                7         4         3

709  +   *-- identity matrix: diagonal matrix with 1s on main diag;
710  +   I = I(3);

                I             3 rows      3 cols    (numeric)

                                1         0         0
                                0         1         0
                                0         0         1

711  +   *-- scalar matrix: diagonal matrix with equal diagonal entries;
712  +   S = diag({10 10 10});

                S             3 rows      3 cols    (numeric)

                               10         0         0
                                0        10         0
                                0         0        10

713  +   *-- unit matrix: all elements = 1;
714  +   J = J(2,5);

                J             2 rows      5 cols    (numeric)

                      1         1         1         1         1
                      1         1         1         1         1

715  +   J = J(3,1);

                J             3 rows      1 col     (numeric)

                                          1
                                          1
                                          1

716  +   *-- zero matrix: all elements = 0;
717  +   Z = J(2,5,0);

                Z             2 rows      5 cols    (numeric)

                      0         0         0         0         0
                      0         0         0         0         0

718  +quit;

Exiting IML.

NOTE: The PROCEDURE IML used 0.22 seconds.

719  +

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